// Copyright 2010 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// package cmplx -- go2cs converted at 2022 March 13 05:42:07 UTC
// import "math/cmplx" ==> using cmplx = go.math.cmplx_package
// Original source: C:\Program Files\Go\src\math\cmplx\pow.go
namespace go.math;

using math = math_package;

public static partial class cmplx_package {

// The original C code, the long comment, and the constants
// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
// The go code is a simplified version of the original C.
//
// Cephes Math Library Release 2.8:  June, 2000
// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
//
// The readme file at http://netlib.sandia.gov/cephes/ says:
//    Some software in this archive may be from the book _Methods and
// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
// International, 1989) or from the Cephes Mathematical Library, a
// commercial product. In either event, it is copyrighted by the author.
// What you see here may be used freely but it comes with no support or
// guarantee.
//
//   The two known misprints in the book are repaired here in the
// source listings for the gamma function and the incomplete beta
// integral.
//
//   Stephen L. Moshier
//   moshier@na-net.ornl.gov

// Complex power function
//
// DESCRIPTION:
//
// Raises complex A to the complex Zth power.
// Definition is per AMS55 # 4.2.8,
// analytically equivalent to cpow(a,z) = cexp(z clog(a)).
//
// ACCURACY:
//
//                      Relative error:
// arithmetic   domain     # trials      peak         rms
//    IEEE      -10,+10     30000       9.4e-15     1.5e-15

// Pow returns x**y, the base-x exponential of y.
// For generalized compatibility with math.Pow:
//    Pow(0, ±0) returns 1+0i
//    Pow(0, c) for real(c)<0 returns Inf+0i if imag(c) is zero, otherwise Inf+Inf i.
public static System.Numerics.Complex128 Pow(System.Numerics.Complex128 x, System.Numerics.Complex128 y) => func((_, panic, _) => {
    if (x == 0) { // Guaranteed also true for x == -0.
        if (IsNaN(y)) {
            return NaN();
        }
        var r = real(y);
        var i = imag(y);

        if (r == 0) 
            return 1;
        else if (r < 0) 
            if (i == 0) {
                return complex(math.Inf(1), 0);
            }
            return Inf();
        else if (r > 0) 
            return 0;
                panic("not reached");
    }
    var modulus = Abs(x);
    if (modulus == 0) {
        return complex(0, 0);
    }
    r = math.Pow(modulus, real(y));
    var arg = Phase(x);
    var theta = real(y) * arg;
    if (imag(y) != 0) {
        r *= math.Exp(-imag(y) * arg);
        theta += imag(y) * math.Log(modulus);
    }
    var (s, c) = math.Sincos(theta);
    return complex(r * c, r * s);
});

} // end cmplx_package
